Question

Q(1) A natural history museum borrows $2,000,000 at simple annual interest to purchase new exhibits. Some of the money is borrowed at 6%, some at 7.5%, and some at 8.5%. Use a system of linear equations to determine how much is borrowed at each rate given that the total annual interest is $137,000 and the amount borrowed at 7.5% is four times the amount borrowed at 8.5%. Solve the system of linear equations using matrices.

Q(2) Use a system of equations to find the cubic function f(x) = ax³ + bx² + cx + d  that satisfies the equations. Solve the system using matrices.

f(−1) = 3

f(1) = 5

f(2) = 30

f(3) = 95

Q(3) An object moving vertically is at the given heights at the specified times. Find the position equation

s = 1/2at² + v₀t + s₀ for the object.

At t = 1 second, s = 136 feet

At t = 2 seconds, s = 108 feet

At t = 3 seconds, s = 48 feet

Answer 1